Radio-frequency actuated polymer based phononic meta-materials for control of ultrasonic waves Ezekiel Walker and Arup Neogi*
Estimation of Frequency shift: The frequency shift is estimated from the reduced frequency, . The center of the first transmission stop gap as a function of is constant, and any shift in the spectrum is a direct result of the increasing sound velocity.
‘k’ is based on the lattice structure. For a square lattice, , where a is the lattice spacing.
For the case where is constant,
If Eq. (S3) is used to examine the band shift in water, by letting
RF was generated and controlled using parallel plates arranged in a capacitor setup. Two coils with 3.03 mH of inductance were coupled with coaxial capable capacitors to produce an open plate oscillator frequency of 318.6 kHz. The RF field voltage across the plates was calculated to be 34.3kV. The base plate was 18 cm x 20 cm, and the top plate was 16 cm x 20 cm. 1 cm of the edges of the top plate was folded down at a 90° angle facing the base plate to reduce the effects of fringe fields. Spacing between the plates was maintained by two 1.5 cm x 2.5 cm x 12 cm Teflon blocks with grooves cut to hold the plates at predetermined heights. For RF tuning, the plates were spaced at 8.5cm, enough to ensure there was no direct electrical conduit into the samples between plate antennae (Figure S1). Each device was placed in the field for RF application. The plates were spaced such that there was no direct electrical conduit through the devices between plate antennae. Placement of the devices into the setup resulted in a feedback induced slight red-shifting of the application frequency to roughly 314 kHz. Ultrasonic spectroscopy was performed at 5 minute intervals over a 120 minute span while RF was continuously applied.
Figure S1 – Schematic of the RF tuning setup for the device. RF is generated using LC harmonic oscillator with coils and capacitors. The setup is a parallel plate antenna setup with no electrical conduit between the samples to ensure all effects are from RF electromagnetic radiation.
RF was generated and controlled using parallel plates arranged in a capacitor setup. Two coils with 3.94 mH of inductance were coupled with coaxial capable capacitors to produce an open plate oscillator frequency of 454.4 kHz. The RF field voltage across the plates was calculated to be 8453V. The plates were 5.9 cm x 3 cm, capped on the edges with Teflon, and placed 3.1 cm apart on opposite sides of the 10-period side of the phononic crystal. Only KBTSC was examined in air. The plates were spaced such that there was no direct electrical conduit through the device between plate antennae. Placement of the device into the setup resulted in a feedback induced red-shifting of the application frequency to roughly 422 kHz. Ultrasonic spectroscopy was performed at 2 minute intervals over a 100 minute span with RF was continuously applied for 50 minutes, then RF off for 50 minutes.
Water-filled phononic crystal
Figure S2 - (S2a) An image of the base phononic crystal utilized for the metamaterial device. (4b) The band diagram for the phononic crystal in water. Only spectra for the k00 () wave was recorded and examined from 450-650 kHz. The analyzed range is well-above the homogenization limit for periodic structures and includes the second transmission band.
Water-only device: The plain phononic crystal (SQSC) is the phononic crystal without any integrated hydrogels in a water ambient medium (Figure S2a). Figure 2a (inset) shows the full measured transmission spectrum from 200 – 800 kHz for SQSC at 0 minutes of RF exposure. The strong peak at 315 kHz is an artefact from the RF signal coupled to the device for control detected due to the configuration of the detection setup. The 1st transmission band is beyond the scope of this work, and ends at 260 kHz. Only the high frequency edge of the 1st transmission band was detected and the analysis focuses mainly on the 2nd transmission band featured in Figure 4.
Figure S3a is the time evolution of the SQSC ultrasonic transmission spectrum at the beginning (0 min.), middle (60 min.), and end (120 min.) of applied RF (left) and a frequency dependent RF modulation factor (M(f,t), right). M(f,t) is defined as
where P(f,t) is the normalized measured signal in Watts at time t. M(f,t) shows the time evolution of ultrasonic transmission over a frequency range with applied RF. High M(f) is indicative of strong RF control of ultrasound.
For the SQSC device, the steel rods are the scatterers, while water is both the ambient and contrasting material for the phononic crystal. A changing sound velocity in low-dispersion contrasting materials generally results in a shifting transmission spectrum with comparatively minimal reshaping of the transmission band [22,4]. RF waves induces heating in water, changing its sound velocity. Figure S3b displays the blue shift in the 2nd transmission in the presence of an RF field. Both the leading and trailing band edges shift about 8 kHz. At the outset of the experiment, there is a partial gap at 505 kHz as the transmission decreases by almost 20 dBm from peak transmission in the band as evidenced by the modulation factor (Figure S3c). The depth of the gap decreases as the water heats from RF application, but the relative position with respect to the band edge is maintained at about 27 kHz. Though the band shifting is technically RF modulation of ultrasonic transmission through the phononic crystal, the lack of change of the elastomorphic or intrinsic mechanical properties of the device itself lends more to be desired in demonstration of RF control.
The frequency shift can be examined by the reduced frequency, as described in the supplementary section. Figure 5 shows a frequency shift of the leading band edge from 470 kHz to 477 kHz, and a trailing band edge from 595 kHz to 603 kHz. A close examination of the shifts of the band features at 505 and 587 kHz reveals similar changes of ~8 kHz, supporting the contention that the contour shape is maintained. The experiment began at 23 °C, corresponding to a sound velocity in water of 1489 m/s. From (S5) the resulting increase in the sound velocity of water as determined by each edge is 1511 m/s and 1509 m/s, which projects to ~32 °C . The RF dissipation factor (DF) discussed in Figure 3 is for pure samples and does not incorporate a thermodynamic model for heat loss, and places an upper bound on the temperature increase (ΔT) that could be attained in the most ideal setup. Based on the DF, the upper bound for ΔT is 32° C for pure water, and falls within observations for the RF application time in this work. Thus the blue-shift of a spectral profile with minimal modification of its contour is an effect of applied RF on the device environment and not a designed function of the device.
SQSC is the phononic crystal component of the device without RF actuated acoustic material interstitially filling the crystal. The spectrum of SQSC blue shifts due to the RF heating the water ambient. Similar shift has also been demonstrated in arrangements where heat was applied to ambient water through other means . The relative contour of the spectral profile is significant. For the temperature increase induced by the RF field, the relative contrast in sound velocity between the stainless steel scatterers and ambient water is maintained over the full spectral range due to water being a low-dispersion medium. It results in a spectral profile that is not significantly changed within the temperature range of interest.
The RF controlled metamaterial devices incorporate poly(N-isopropylacrylamide)-based hydrogel as the contrasting material to stainless steel scatterers in a phononic crystal. Standard free-radical polymerized PNIPAm has insufficient RF sensitivity to be controlled with an RF stimulus. To remedy this issue, high-k dielectric nanoparticles of 10% KF-BaTiO3 (KBT) calcined at 800° were dispersed into the hydrogels with the addition of pre-polymerized poly (vinyl alcohol) (PVA) as a thickening agent for the monomer solution. Examination of the dielectric properties combined with the thermal conduction and density surprising resulted in PVA being a superior material for RF susceptibility (Figure 3). The PVASC is analyzed and observations given below.
Figure S4 depicts the transmission properties of PVASC (Figure 6b) ultrasonic transmission spectra. Both devices that incorporate PVA modified PNIPAm-based hydrogels exhibit strong RF control of ultrasound as evidenced by the dynamic behavior of the transmission bands of each. Figure S4a depicts the second transmission band (~490 kHz - ~615 kHz) at 0 min (black), 60 min (blue), and 120 min (green) of RF stimulus. Unlike SQSC, the low-frequency band edges for both KBTSC and PVASC shift minimally (<3 kHz). The width of the band expands 26 kHz at the -10 dB points from peak transmission for an expansion of 35% (Figure S4b). The strong variation in intraband feature intensity at a large range of frequencies in Figure S4b arises due to local resonances that a functions of the highly dispersive elastomechanical contrast between the stainless steel scatterers and PVA PNIPAm. RF application increases the temperature of water, but also couples to the composites to change elastic material parameters while inducing volumetric phase change in the devices that create pockets of hydrogel.
RF modulation of ultrasonic transmission in the device is represented for a select frequency range in Figure S4c. M(f) reaches in excess of 110 for frequency ranges near 603 kHz and 618 kHz, with multiple other ranges shows still significant modification. The desired property for RF control of ultrasound in these devices is the reshaping of the transmission band as it results from the change of the elastomorphic or material mechanical properties. Both Figures 6 and 7 strongly support this characteristic as the time dependent RF wave application significantly affects the ultrasonic transmission through the structure. Based on the DF and intraband modulation of PVASC, PVASC seems to perform superior to KBTSC in both actuation time and RF modulation intensity.
Investigation of the dielectric-hydrogel composite confirmed the addition of KF-BaTiO3 nanoparticles calcined at 800 °C to greatly enhance the dielectric properties of the composite. More critically, the volumetric phase change capabilities were also maintained with the addition of the nanoparticles and modifications to the PNIPAm synthesis process. However, compared to the nanoparticle-free PVA hydrogel, the enhancement in the dissipation factor of KBT hydrogel due to ε’ and tan δ was offset by its relatively higher specific heat. The optimal additive dielectric for the RF acoustic material maintains both high dielectric constant and loss characteristics combined with low-density and low specific heat. Both PVA and KBT hydrogels were superior to free-radical polymerized bulk poly(N-isopropylacrylamide) hydrogels, with dissipation factors of the same order of magnitude as water compared to bulk PNIPAm which is a magnitude smaller. The dispersive elastomechanical properties of the RF responsive acoustic materials allow for delineation of RF induced effects on the device environment from the intended effects for the metamaterial device.
Bulk PNIPAm has dispersive elastic bulk and shear modulus as indicated by its anomalous speed of sound as a function of both temperature and frequency . Though RF affects the ambient device environment, it also couples strongly to the PNIPAm based acoustic materials as exhibited by the DF in Figure 3. The estimated temperature attained in SQSC is solidly in the range where PNIPAm undergoes significant variation in its elastic constants as indicated by the anomalous behavior in the sound velocity shown in Figure 1b. Unlike in the low or non-dispersive case of water, the effective frequency dependence of the elastic properties of PNIPAm manifests as a dispersive change in the elastic contrast between the stainless steel scatterers and hydrogel. The effects on the spectral contour in the second band are significant as both PNIPAm-based devices lack the shifting observed in the SQSC case, undergo expansion of up to 35%, and possess ephemeral features such as the temporary pseudoband at 538 kHz in the KBT device. For these devices, the RF induced spectral contour changes distinguishable from SQSC implies the effective coupling of control of transient ultrasound to RF. This is contactless control of transient ultrasound in a large, macroscopic metamaterial device by design. It also provides a design mechanism through which light can be used to modulate other metamaterial devices such as acoustic cloaks lenses, waveguides, or cavities.